Struggling with a Complex Partial Differential Equation: Can You Help?

[the_edge]

Hello, I'm new at these equations so I need help. I'm not able to solve this partial differential equation, if there is somebody who can help me do it pleasez...

http://galeb.etf.bg.ac.yu/~ii030168d/problem/problem.GIF

OK, it begins like this:

http://galeb.etf.bg.ac.yu/~ii030168d/problem/problem1.GIF

But I don't know what to do next... This problem is from exam on my faculty. (I haven't pass)


I would appreciate any help...

 

[arildno]

Well, the first equation may be rewrittent as a ratio between the differentials of x and y as follows:
$$\frac{dy}{dx}=\frac{x-y-x^{2}y}{x+y+xy^{2}}$$
I'm not sure if this is analytically solvable, though..

 

[arildno]

You MIGHT try changing of variables u=x+y, v=x-y; possibly, that will simplify the expressions.

 

[the_edge]

Sorry I made a mistake, problem is next:

dx/(x+y-xy^2) = dy/(x^2y-x-y) = dz/(z(y^2-x^2))

Maybe now there is solution. Those changes can't help, they wouldn't simplify the expression, but thanks...